Field of the Invention
This invention relates to teaching tools for the teaching, learning, and assessing of student understanding of Science, Technology, Engineering and Mathematics (STEM) subjects, and, more particularly, relates to tools which utilize a touch sensitive computer screen to teach, learn, and assess student understanding of STEM subjects.
Description of Related Art
In the field of education, devices or systems of cooperating devices which are used to enhance teaching and learning are commonly referred to as either teaching tools or teaching interventions. Furthermore, the evaluations of certain aspects of an educational process, such as subject matter questions or achievement tests administered to students, are commonly referred to as assessments.
Currently, various tools or interventions, as they are called in the art, are used to teach and motivate the learning of mathematical and physical concepts. These tools include chalkboard, whiteboard, graphing calculator, personal computers, pen-enabled tablet computers, Interactive Whiteboards (IWB), computational mathematics engines, concept visualization software tools, and the experimental laboratory. Whereas each of these tools individually engages students in its own way, a physical disconnect exists between them. For example, a graphing calculator is separate and distinct from a chalkboard and each of these tools requires different expertise to use. When a teacher switches from tool to tool, the change interrupts the flow of teaching and distracts students.
Recently, mobile tablets with touch sensitive screens (for example, iPad™ devices, Android™ devices, and similar devices), because of their low cost, are becoming ubiquitous in classroom environments. Teachers and students are using the didactic features of tablets to teach and learn STEM subjects wherein notation is an important requirement. For example, entering a math notation, such as
      x    =                            -          b                ±                                            b              2                        -                          4              ⁢                                                          ⁢              ac                                                  2        ⁢                                  ⁢        a              ,is more difficult and time consuming when entering these types of expressions into a computer using a keyboard and mouse compared to a user inputting the touch sensitive screen of a tablet with a stylus or fingertip, as if using paper and pencil.
Teachers of STEM subjects recognize the need to visually reinforce students' understanding of abstract concepts as these concepts are being presented in a classroom environment. Furthermore, since most STEM problems are solved with step by step solutions, it is important that students understand and visualize how step by step solutions are created. Presently, most teaching systems and methods which include a visualization component require teachers to switch tools during class—one tool to present lesson content and another to provide visual reinforcement. For example, a teacher may use a chalkboard or a whiteboard to present a step by step solution and a graphing calculator to visually reinforce it.
There is a need in the art for a single multifunctional tool which can be used by a teacher to not only present the steps of a step by step solution but also provide simultaneous reinforcement thereof using a system and a method which does not interrupt the flow of teaching. A single tool is needed which is easy to learn and easy to use and which does not require hours of training to learn a new programming language. Using the teaching tool of the instant invention is as simple as working with pencil-and-paper. It evaluates the correctness of each step of a step by step solution and automatically color codes each step to provide a graphical overview of a complete solution, all without interrupting the flow of teaching.
What follows are descriptions of products which are known in the industry and which are currently available as computerized teaching interventions for the teaching of STEM subjects:
Graphing calculators have been widely adopted in classrooms because of their computational power, but they require significant training before users (both students and teachers) become experts at finding the complicated sequence of button pushes needed to solve and graph problems.
Microsoft Math™ embodies graphing calculator software targeted toward use in math education. Even though its interface is tablet PC enabled and incorporates rudimentary entry of handwritten math, it is not a fully pen-centric application. The application requires keyboard entry for effective use. Also, the Microsoft Math™ software product does not offer ease of entry of mathematical notation, interface commands and free-form drawings.
XThink's MathJournal™ is a Tablet PC application for the type of mathematical problem solving that is performed by engineers and scientists rather than students. It focuses on functionality rather than on an uninterrupted teaching experience.
Interactive Physics™ and The Geometer's SketchPad™ require users to learn an unfamiliar WIMP-based (Windows, Icons, Menu's, Pointers) visual language. This unfamiliar, as compared to pencil and paper, style of interaction makes these programs inaccessible to many casual users, and presents significant usage barriers for classroom and problem solving settings.
Systems such as Mathematica™, Maple™, Matlab™, and MathCad™ are focused primarily on entering mathematics for computation, symbolic mathematics, and illustration. These tools require complex scripting languages for mathematical entry. Although these languages use mathematical notation, they are one dimensional and require unconventional keyboard-based entry which is much less intuitive than using 2D handwritten mathematics. None of these systems let the user create diagrams on the screen of a computer in a natural pencil-and-paper style.
FluidMath™ provides a system for the teaching and learning of STEM subjects through the use of handwritten input into pen-enabled computers. FluidMath™ enables the user of a tablet PC to create, solve, and explore STEM principles all in his or her own handwriting as if working with pencil and paper. However, FluidMath™ does not teach a system which color codes each step of a step by step solution to a STEM problem handwritten on the touch sensitive screen of a tablet PC.
There are also a number of U.S. patents which disclose teaching systems and methods. For example, U.S. Pat. No. 5,176,520 which issued to Eric Hamilton on Jan. 5, 1993, discloses a computer-assisted instructional information delivery system having at least two stations—one station for an instructor and one or more stations for students. An interactive monitor is positioned in each station. Each interactive monitor displays instructional information in visual form as inputted by a stylus or light pen on the interactive monitor. A network communication system operated by a central processing unit and corresponding software communicates the instructional information from the stylus as inputted on one of the interactive monitors and selectively displays the instructional information simultaneously and concurrently onto any or all of the interactive monitors of the stations. Hamilton does not disclose a system which automatically evaluates the correctness of the instructional information input into the interactive monitors.
U.S. Pat. No. 6,760,748, which issued to Omar Hakim on Jul. 6, 2004, discloses an interactive electronic instructional system as a teaching interface between a teacher and students where data is transmitted from the teacher's terminal to the students' terminals. The data is received at the student terminals and is separated into execution data and instructional data. The student terminals are grouped into teams allowing student teams to interact with a group decision. This encourages team participation by shy or otherwise reluctant students. Team answer data is transmitted from one of the student terminals in the team to the teacher's terminal. The teacher monitors team answer data to infer class progress towards a goal. The teacher may modify the instructional data based on the progress. Hakim does not disclose a system which automatically produces feedback regarding the correctness of each step of a step by step solution to a STEM problem.
U.S. Patent Application Publication No. 2006/0024649 issued to David H. Vernon on Feb. 6, 2006 discloses a handheld device, typical of a graphing calculator, for aiding students in solving mathematical problems. Rather than solving the problem for the student it provides a graphical environment where students can step through the solution process. The problems and their solutions are entered into the devices by pushing buttons on the face of the device. The invention enforces the hard and fast rules of arithmetic and mathematics as the student performs steps in solving a problem and notifies the student via a text message shown on a screen on the face of the device when those rules are violated. Vernon does not disclose a system which understands whether handwritten math notation input is correct.
U.S. Pat. No. 7,213,211, which issued to Sanders et al. on May 1, 2007, discloses a system for knowledge transfer in a group setting and comprises a plurality of participant work areas and a moderator work area. Each of the plurality of participant work areas has at least one corresponding participant input-device, and each of the participant input-devices is adapted to define participant images that are then included on the corresponding participant work area. The moderator work area comprises at least one moderator input-device. The at least one moderator input-device is adapted to define moderator images that are then included on the moderator work area and to select moderator images that are then simultaneously included on each of the plurality of participant work areas. The moderator input-device is further adapted to select participant images from any of the plurality of participant work areas that are then included on the moderator work area. Sanders does not teach work areas which receive handwritten input drawn on the screen of a tablet PC.
U.S. Pat. No. 7,466,958, which issued to Dunk et al. on Dec. 16, 2008, discloses an on-line teaching and learning system with rapid change-by-change or real-time reinforcement of student responses to math questions, including monitoring by the teacher of the actual responses as well as their correctness. Equations or expressions are entered by selecting one or more symbols from a menu, selecting one or more symbols using buttons in the application, using one or more hotkeys, and/or entering information in a character bases syntax. Dunk et al. does not disclose a system which accepts, recognizes and evaluates handwritten math notation input.
U.S. Pat. No. 7,752,148 which issued to Yu et al. on Jul. 6, 2010 discloses a problem checker architecture that monitors user progress during a problem-solving process and assists the user through the process (e.g., when requested) using common human methods of solving the problem. Assistance can be in the form of detecting errors during the process, and providing context-sensitive help information when the user gets stuck or makes a mistake. The problem checker comprises an input component for receiving a math problem to be worked via a solving process and a problem checker for monitoring the process and generating context-sensitive information as part of the solving process wherein the context-sensitive information includes at least one of hint information, correction information, or a solution generated in response to a user action during the solving process. Yu does not teach a means to color code each step of a step by step solution.
The above-noted products and U.S. patents do not disclose systems which enable teachers to teach solutions to STEM problems by combining the use of pen-enabled computers with spontaneous handwritten input of math notation. The prior art does not teach a means for color coding the steps of a step by step solution to STEM problems as each step is being written on the screen of a pen-enabled computer and it does not teach a means for providing instant feedback regarding the correctness of each step. Moreover, there is no prior art, of which we are aware, that discloses a system and a method enabling teachers to create a fully color coded step by step solution thereby visually defining all of the steps of the solution. There is a need in the art for an intervention wherein a teacher can provide instant visual feedback to his/her students regarding the correctness of each step of a solution to a problem as they are being presented in class. There is also a need in the art for a system which enables teachers to generate a fully color coded step by step solution to STEM problems in order to help students gain a deeper understanding of the process used to derive the solution. Finally, there is a need in the art for an intervention wherein students, when exploring problems on their own, are provided instant visual feedback as to the correctness of each step of their solutions and are also provided a color coded linkage between all the steps of their complete solution.